Quantum Group Schrödinger Field Theory

Abstract

We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size $\Delta x=(1-q)x$. Then, based on this, we develop the basic formalism of quantum group Schrödinger field theory in one spatial quantum dimension, and explicitly exhibit the $S{U}_q(2)$ covariant algebras satisfied by the $q$-bosonic and $q$-fermionic Schrödinger fields. We generalize this result to an arbitrary number of fields.

11 pages,LaTeX, LTP-035-UPR

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• $g{l}_q(n)$-covariant Oscillators and q-Deformed Quantum Mechanics in n Dimensions
• Remarks on SU_q(2) fermions